Square Root of 149

The square root of 149 is expressed as √149 in the radical form and as (149)^½ or (149)^0.5 in the exponent form. The square root of 149 rounded up to 5 decimal places is 12.20656. It is the positive solution of the equation x² = 149.

• Square Root of 149: 12.206555615733702
• Square Root of 149 in exponential form: (149)^½ or (149)^0.5
• Square Root of 149 in radical form: √149

• The square root of 149 is written as (149)^1/2 in the exponential form.
• The square root of 149 is written as √149 in the radical form.
• The square root of 149 in the decimal form is 12.2065

The square root of 149 is not an integer.
A rational number is defined as a number that can be represented in the ratio of two integers (p/q) where q ≠ 0. Since the square root of 149 cannot be written in the form of p/q, it is an irrational number.

We will now calculate the square root of 149 using the following methods:

Square Root of 149 Using Approximation Method

• Find two consecutive perfect squares between which 149 lies.
  In the case of 149, the perfect squares are 144 (12²) and 169 (13²).
  Thus, the whole number part of the square root of 149 is 12.
• Now, for the decimal part, we will use the below formula:
  (Given number – Smaller perfect square) / (Greater perfect square – smaller perfect square)
  = (149 – 144)/(169 – 144) = 5/25 = 0.20
• Hence, the approx. value of the square root of 149 by the approximation method is 12.20

Square Root of 149 By Long Division

With the help of the following steps, we can calculate the square root of 149 by the long division method.

• Start pairing the digits by placing a bar on top of them from the unit’s place in pairs of two. In the case of 149, we will have two pairs 49 and 1(pairing from the right).
• Now, find a number(N) whose square is ≤ 1. The value of N will be 1 as 1 × 1 = 1≤ 1.
• We get the quotient (1). Add the divisor N (1) with itself and we get the new divisor as 2N (2).
• Drag the next pair of numbers down. The new dividend is 049. Find a number (q) such that 2q × q ≤ 49. The value of q will be 2.
• Now, put a decimal in the dividend at the end of 149 and in the quotient at the end of 12. Also, place 3 pairs of zeros in the dividend after the decimal.
  Repeat the above steps for the remaining three pairs of zero.

So, we get the value of the square root of √149 = 12.206 by the long division method.

Explore square roots using illustrations and interactive examples: 

• Square root of 144
• Square root of 89
• Square root of 45
• Square root of 49
• Square root of 7

• The square root of 149 is an irrational number.
• The number 149 is not a perfect square.
• The square root of -149 is an imaginary number.